Quantum complexity, as a concept originated from quantum computation, plays an important role in the study of quantum gravity in recent years. It measures the number of simple quantum gates in a quantum circuit. Complexity analysis is a useful way to understand the firewall puzzle [1]}, which is known as the Harlow-Hayden conjecture [2]}. As a boundary observable, it's conjectured that the gravitational dual of complexity is the volume or the action in the bulk, and can be used to probe the interior of black holes [3]}, [4]}. For other applications of complexity to understand quantum gravity, see e.g. [5]}, [6]}, [7]}, [8]}, [9]}.
